198267970563 · 6007# + 7811555753
(Another of the Prime Pages' resources)
The Largest Known Primes Icon
  View this page in:   language help
 

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.

This prime's information:

field (help)value
Description:198267970563 · 6007# + 7811555753
Verification status (*):PRP
Official Comment:Consecutive primes arithmetic progression (4,d=30), ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):x38 : Broadhurst, Primo, OpenPFGW
Decimal Digits:2575   (log10 is 2574.5024760905)
Rank (*):86887 (digit rank is 5)
Entrance Rank (*):79241
Currently on list? (*):short
Submitted:10/16/2013 16:29:18 CDT
Last modified:10/16/2013 16:50:31 CDT
Database id:115996
Status Flags:Verify, TrialDiv
Score (*):28.2242 (normalized score 0)

Archival tags:

There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper.  Such primes are tracked with archival tags.
Consecutive Primes in Arithmetic Progression (archivable class *)
Prime on list: yes, rank 5
Subcategory: "Consecutive primes in arithmetic progression (4,d=*)"
(archival tag id 217307, tag last modified 2013-10-25 14:50:55)
Arithmetic Progressions of Primes (archivable class *)
Prime on list: no, rank 139, weight 37.2824300794624
Subcategory: "Arithmetic progression (4,d=*)"
(archival tag id 217308, tag last modified 2017-08-19 13:50:02)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 598
Subcategory: "ECPP"
(archival tag id 217309, tag last modified 2017-09-09 11:20:24)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

David Broadhurst writes (11 Sep 2014): 
certificates

Verification data:

The Top 5000 Primes is a list for proven primes only. In order to maintain the integrity of this list, we seek to verify the primality of all submissions.  We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial divide and PRP check every entry before it is included in the list.
fieldvalue
prime_id115996
person_id9
machineDitto P4 P4
whatprp
notesCommand: /home/ditto/client/pfgw -tc -q"198267970563*6007#+7811555753" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 198267970563*6007#+7811555753 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 3+sqrt(11)
Calling N-1 BLS with factored part 0.51% and helper 0.14% (1.68% proof)
198267970563*6007#+7811555753 is Fermat and Lucas PRP! (2.5821s+0.0005s)
[Elapsed time: 3.00 seconds]
modified2013-10-21 18:10:45
created2013-10-16 16:48:53
id161488

Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.